Calculating the constants of a permanent-magnet DC motor

Based on measurements (current and angular velocity dependent on a given voltage from 0 to 12V) and force dependant on a given current (0 to 2A), I want to calculate the armature resistance, torque constant and the generator constant. The rotor radius is given too.

My approach

Armature resistance
Using the method of least squares, I calculate a linear function. $$\I = f(U)\$$
The Resistance equals the reciprocal of the slope of the function (red).

$$I = \frac{U}{R}$$

I know that my calculated value for R should be correct.

torque constant
I calculate the linear function $$\M=f(I) \Rightarrow F \cdot r = f(I)\$$.
The slope of this function equals the torque constant. I don't know, if my calculated value is correct. Can you tell me if my approach sounds good?

generator constant
That's my main problem.
The idea was to use the equation $$\ U_i = c \cdot \omega \$$
Since $$\U_i\$$ wasn't measured, I have to calculate it.
$$\U_i = U-I_R \cdot R \$$ Where $$\U\$$ is the input voltage, R is the calculated resistance from before and $$\I_R\$$ is the measured current.
Plotting this, I realized that I am doing something wrong. It seems that there is some major issue in my approach but I can't find it.

**Edit: ** I added the other plots. The blue line displays the real data. The red line displays the "linearized" values, computed with the method of least squares.
The searched value was always expected as the slope (or the reciproce) of the (red) graph.

• Are you calculating the resistance using voltage and currents measured when the rotor is locked? Or when it's free to spin? The latter, you need to consider back EMF. Commented May 16, 2021 at 15:03
• a graph right out of quantum physics ... lol Commented May 16, 2021 at 15:52
• @Hearth unfortunately I can't answer this question. As you maybe can guess it yourself, it's a (college) exercise. Due to the pandemic, I couldn't measure by myself and I have no information how the data were collected. Since it's sunday I can't get this information right now. Because R seems to be correct (should be arount 5.5Ohms and is exactly 5.4965Ohms), I would guess that the rotor was locked. Based on the data I have, what would be the approach IF the rotor wasn't locked and otherwise how would it look like, if the rotor was really locked? Commented May 16, 2021 at 17:53
• I can promise you it's not exactly 5.4965 Ω, that's far too precise a measurement for how this data was probably taken. But it sounds like these are locked-rotor measurements if the value you get is close to what you expect. Commented May 16, 2021 at 18:02
• You will be right! The value is just the value that Matlab spit out as the slope of the graph. I added the other missing plots. Maybe it helps. Commented May 16, 2021 at 18:19

All those measurements are to be done with a locked rotor, i.e. $$\\omega=0\$$, so there is no BEMF involved. But you could try to express the torque constant as voltage constant:
$${\displaystyle K_{\text{T}}={\frac {\tau }{I_{\text{a}}}}={\frac {60}{2\pi K_{\text{v(RPM)}}}}={\frac {1}{K_{\text{v(SI)}}}}}$$